Operator's, How to detect `MOUSEMOVE` inside of `LEFTMOUSE` event
If event.type is LEFTMOUSE, how could it be MOUSEMOVE at the same time?
(exclude quantum mechanics)

The modal() method is called for every event, so you need to "remember" the left mouse state for the subsequent calls on MOUSEMOVE events:

import bpy
from bpy.props import IntProperty, FloatProperty


class ModalOperator(bpy.types.Operator):
    """Move an object with the mouse, example"""
    bl_idname = "object.modal_operator"
    bl_label = "Simple Modal Operator"

    first_mouse_x = IntProperty()
    first_value = FloatProperty()

    def modal(self, context, event):
        if event.type == 'MOUSEMOVE':
            if self.lmb:
                delta = self.first_mouse_x - event.mouse_x
                context.object.location.x = self.first_value + delta * 0.01

        elif event.type == 'LEFTMOUSE':
            # we could handle PRESS and RELEASE individually if necessary
            self.lmb = event.value == 'PRESS'

        elif event.type in {'RIGHTMOUSE', 'ESC'}:
            context.object.location.x = self.first_value
            return {'CANCELLED'}

        return {'RUNNING_MODAL'}

    def invoke(self, context, event):
        # variable to remember left mouse button state    
        self.lmb = False

        if context.object:
            self.first_mouse_x = event.mouse_x
            self.first_value = context.object.location.x

            context.window_manager.modal_handler_add(self)
            return {'RUNNING_MODAL'}
        else:
            self.report({'WARNING'}, "No active object, could not finish")
            return {'CANCELLED'}


def register():
    bpy.utils.register_class(ModalOperator)


def unregister():
    bpy.utils.unregister_class(ModalOperator)


if __name__ == "__main__":
    register()

    # test call
    bpy.ops.object.modal_operator('INVOKE_DEFAULT')